battery charged at 12.7 V, not getting power to the RV??

Lots of questions. First of all, were you plugged into shore power (commercial power)? How old is the RV and what brand and model? Does any of the other 12v equipment work? Such as the vent fans. When you turn on the second light and everything quits, does this include other 12v equipment? Sounds like the converter/charger is bad but without further information, that is a guess. First of all I would check the ground wires to the trailer frame and to the converter where ever it is.